I'm using the kinetics toolkit in Python (https://kineticstoolkit.uqam.ca/doc/) to process marker data. It provides convenient conversion of marker data to reference frames, from which it will calculate matrixes for homogeneous relative angles between frames. It will then translate the homogeneous relative angles to Euler angles to give the standard way of describing joint angles.

I'm interested in getting angular velocity for the joints as well. I understand from the papers referenced below that matrixes for the derivatives of the homogeneous relative angles can be calculated using some fairly straightforward matrix algebra.

Two things I want to know:

1. Can the same function which extracted Euler angles from the homogeneous matrix be used to extract Euler angles from its derivative?

2. Is there a Python function or some sample code which calculates the derivatives of the homogeneous matrixes so I don't reinvent the wheel

Thanks,

Opher

Giovanni Legnani, Federico Casolo, Paolo Righettini, Bruno Zappa, A homogeneous matrix approach to 3D kinematics and dynamics — I. Theory, Mechanism and Machine Theory. Mechanism and Machine Theory 31(5):573-587, 1996

https://doi.org/10.1016/0094-114X(95)00100-D.

Giovanni Legnani, Federico Casalo, Paolo Righettini, Bruno Zappa, A homogeneous matrix approach to 3D kinematics and dynamics—II. Applications to chains of rigid bodies and serial manipulators, Mechanism and Machine Theory 31(5):589-605, 1996.

https://doi.org/10.1016/0094-114X(95)00101-4.

I'm interested in getting angular velocity for the joints as well. I understand from the papers referenced below that matrixes for the derivatives of the homogeneous relative angles can be calculated using some fairly straightforward matrix algebra.

Two things I want to know:

1. Can the same function which extracted Euler angles from the homogeneous matrix be used to extract Euler angles from its derivative?

2. Is there a Python function or some sample code which calculates the derivatives of the homogeneous matrixes so I don't reinvent the wheel

Thanks,

Opher

__References:__Giovanni Legnani, Federico Casolo, Paolo Righettini, Bruno Zappa, A homogeneous matrix approach to 3D kinematics and dynamics — I. Theory, Mechanism and Machine Theory. Mechanism and Machine Theory 31(5):573-587, 1996

https://doi.org/10.1016/0094-114X(95)00100-D.

Giovanni Legnani, Federico Casalo, Paolo Righettini, Bruno Zappa, A homogeneous matrix approach to 3D kinematics and dynamics—II. Applications to chains of rigid bodies and serial manipulators, Mechanism and Machine Theory 31(5):589-605, 1996.

https://doi.org/10.1016/0094-114X(95)00101-4.

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